Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Sketch the Graph of the Function
To sketch the graph of the function \( f(x) = -x + 4 \), follow these steps:
1. **Create a Table of Values:**
Given the function \( f(x) = -x + 4 \) and the range \( -4 \leq x \leq 4 \), compute the values of \( f(x) \) for selected values of \( x \) within this interval.
| \( x \) | \( f(x) = -x + 4 \) |
|--------|---------------------|
| -4 | |
| -3 | |
| 0 | |
| 1 | |
| 3 | |
| 4 | |
2. **Enter the values of \( f(x) \) in the table above:**
- When \( x = -4 \):
\[ f(-4) = -(-4) + 4 = 4 + 4 = 8 \]
- When \( x = -3 \):
\[ f(-3) = -(-3) + 4 = 3 + 4 = 7 \]
- When \( x = 0 \):
\[ f(0) = -0 + 4 = 4 \]
- When \( x = 1 \):
\[ f(1) = -1 + 4 = 3 \]
- When \( x = 3 \):
\[ f(3) = -3 + 4 = 1 \]
- When \( x = 4 \):
\[ f(4) = -4 + 4 = 0 \]
The completed table of values:
| \( x \) | \( f(x) = -x + 4 \) |
|--------|---------------------|
| -4 | 8 |
| -3 | 7 |
| 0 | 4 |
| 1 | 3 |
| 3 | 1 |
| 4 | 0 |
3. **Sketch the Graph:**
Plot the points from the table on the graph:
- (-4, 8)
- (-3,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5abeb1f-981a-477d-b103-3469d09f5043%2F4a927b60-d1a4-458a-bbd1-b00ce3ced8f2%2Fbtddavm_processed.png&w=3840&q=75)
Transcribed Image Text:### Sketch the Graph of the Function
To sketch the graph of the function \( f(x) = -x + 4 \), follow these steps:
1. **Create a Table of Values:**
Given the function \( f(x) = -x + 4 \) and the range \( -4 \leq x \leq 4 \), compute the values of \( f(x) \) for selected values of \( x \) within this interval.
| \( x \) | \( f(x) = -x + 4 \) |
|--------|---------------------|
| -4 | |
| -3 | |
| 0 | |
| 1 | |
| 3 | |
| 4 | |
2. **Enter the values of \( f(x) \) in the table above:**
- When \( x = -4 \):
\[ f(-4) = -(-4) + 4 = 4 + 4 = 8 \]
- When \( x = -3 \):
\[ f(-3) = -(-3) + 4 = 3 + 4 = 7 \]
- When \( x = 0 \):
\[ f(0) = -0 + 4 = 4 \]
- When \( x = 1 \):
\[ f(1) = -1 + 4 = 3 \]
- When \( x = 3 \):
\[ f(3) = -3 + 4 = 1 \]
- When \( x = 4 \):
\[ f(4) = -4 + 4 = 0 \]
The completed table of values:
| \( x \) | \( f(x) = -x + 4 \) |
|--------|---------------------|
| -4 | 8 |
| -3 | 7 |
| 0 | 4 |
| 1 | 3 |
| 3 | 1 |
| 4 | 0 |
3. **Sketch the Graph:**
Plot the points from the table on the graph:
- (-4, 8)
- (-3,
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